Introduction to Knot Theory

December 7th, 2015

29aug03aThis site contains information on the lecture “Knots” given in autumn 2015 at Cardiff University, School of Mathematics.



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Organisational matters



Many resources on knot theory exist, from classical textbooks over lecture notes to picture galleries, videos and software. Here I list a few of them.


Lecture Notes



  • Unraveling of a complicated looking knot into the unknot.
  • Animation of a Brunnian link.
  • A youtube channel with some introductory videos on knot theory, by Carlo H. Séquin from UC Berkeley.


  • KnotPlot A versatile programme for visualising knots and manipulating them, including some functions to compute mathematical invariants and several educational demonstrations. Has a free trial version. The website also hosts many pictures of knots in space — all pictures of knots displayed on this site are made with knotplot.
  • A collection of knot theory demonstrations, interactive with the Wolfram CDF Player.
  • The Mathematica Knot Theory Package. See also here.


Here you can download the exercise sheets of this course.

Website with all exercises.

In addition to the exercises, I also offer some quizzes consisting of quick questions for you to test your understanding of the material presented in the lecture:

Knot Quizzes


Here you find a list of all the topics covered in the lecture. This list just serves as a reminder of what has been discussed, it is not a replacement for a book/lecture notes.